Universal description of dissipative Tomonaga-Luttinger liquids with SU(N) spin symmetry: Exact spectrum and critical exponents

PT -symmetric, non-Hermitian quantum many-body physics—a methodological perspective

“…However, others employ the alternative ones described in the present subsection [49,56,58,[89][90][91][92][93]. Some even present results for expectation values of observables obtained by both definitions in a single paper [78,79,81,84,94]. One of the central goals of this review is to contribute to a resolution of this conflict.…”

“…For these reasons the above definitions are used in mathematical physics [9,23] and non-Hermitian quantum field theory [9,[71][72][73][74][75]. They have also been adopted by parts of the condensed matter community to study quantum many-body systems [76][77][78][79][80][81][82][83][84] and non-Hermitian topological systems [10,11,85,86]. 17 However, the above postulates of a PT -symmetric observable and of a PT -symmetric 'expectation value' have limiting weaknesses which cannot be ignored.…”

“…This does not seem to be the case. We are not aware of a single work in which a PT -symmetric observable (besides the energy) was measured or in which a potential way how to measure such was described [81]. From the perspective of physics the formalism of PT -symmetric quantum mechanics does not appear to be the first choice however beautiful it may seem mathematically.…”

“…These ideas have recently been extensively investigated in the context of PT -symmetric quantum mechanics, unveiling new kinds of criticality, universality, and symmetry breaking [15,16,32,48,58,77,81,89,97,[107][108][109][110][111][112][113][114]. At this point we refrain from diving into this advanced topic and focus on the methodological aspects.…”

Transfer learning from Hermitian to non-Hermitian quantum many-body physics

“…non-Hermitian models have initially focused on single-particle models [62][63][64][65][66][67][68][69][70][71][72][73][74][75][76][77][78][79][80], and its extension to the fully interacting realm has also gained attention recently [81][82][83][84][85][86][87][88][89][90][91][92][93][94][95][96][97]. Aside from these case studies, unraveling the physics of interacting non-Hermitian systems remains an open challenge due to the scarcity of exactly solvable models, and as conventional (Hermitian) many-body methods cannot be directly applied to the non-Hermitian limit.…”